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Equisingularity in pencils of curves on germs of reduced complex surfaces
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 3 / August 2024
- Published online by Cambridge University Press:
- 04 June 2024, pp. 990-1012
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We study pencils of curves on a germ of complex reduced surface
$(S,0)$. These are families of curves parametrized by 
$ \mathbb{P}^1 $ having 0 as the unique common point. We prove that for 
$w\in \mathbb{P}^1$, the corresponding curve of the pencil does not have the generic topology if and only if either the corresponding curve of the pulled-back pencil to the normalized surface has a non generic topology or w is a limit value for the function 
$ f/g $ along the singular locus of 
$(S,0)$, where f and g are generators of the pencil.
Equisingular Deformations of Sandwiched Singularities
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- Journal:
- Compositio Mathematica / Volume 138 / Issue 2 / September 2003
- Published online by Cambridge University Press:
- 04 December 2007, pp. 199-231
- Print publication:
- September 2003
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